THE SETUP
A Circular Maze organises cells in concentric rings. Each cell touches up to four neighbours: the adjacent cell inward (toward the centre), the adjacent cell outward (toward the edge), and the two cells beside it within the same ring. The innermost ring has no inward neighbour; the outermost ring has no outward neighbour.
Your task is the same as all Number Mazes: place every integer from 1 to N exactly once so that consecutive integers are always adjacent. The result is a single connected path threading through every cell of every ring exactly once.
THE INNER RING IS THE BOTTLENECK
On a rectangular grid, corners are the most constrained positions — two neighbours each. On a Circular Maze, the innermost ring plays the same role. The ring contains a small number of cells (often 4–8), none of which have an inward neighbour. Any path segment entering the inner ring must also exit the inner ring, and the limited cell count means very few routes are available.
Start every Circular Maze solve by examining the inner ring. If any clue number sits in the inner ring or crosses the boundary between ring 1 and ring 2, that clue is the most constrained anchor in the puzzle. Forced segments at the inner boundary frequently propagate outward through several rings before any gap counting is needed.
As a rule of thumb: the smaller the inner ring, the more it dominates the solve. A 4-cell inner ring leaves almost no routing choice for any path that passes through the centre.
RINGS WRAP AROUND
Unlike a rectangular grid, each ring is a loop. The first and last cell in any ring are adjacent to each other — the ring closes back on itself. A path that seems to reach a dead end at one point in a ring can continue by wrapping to the other side.
This wrap-around behaviour is the most common source of wrong placements for new solvers. Before eliminating a candidate route, always check whether the path can continue by going the long way around the ring rather than the short way. The distance looks longer visually but costs exactly the same number of steps.
GAP ANALYSIS AND DEAD-END CASCADES
Between consecutive given clues, the path must thread a fixed number of intermediate cells — the gap. Gaps that span the inner ring boundary are the most useful: the small cell count in the inner ring severely limits which routes fit.
After placing any cell, scan its neighbours for near-dead-ends — cells with only one remaining free neighbour. In a Circular Maze, these appear frequently near ring boundaries, where the inward and outward neighbours fill in faster than the within-ring neighbours. Cascade dead-ends immediately; one forced move near the inner ring often propagates through three or four cells in sequence.
HOW IT COMPARES TO OTHER MAZE VARIANTS
Circular Maze uses the same four-direction adjacency as Square Maze — the difference is entirely in topology. Where Square Maze corners provide two-neighbour constraint, Circular Maze provides it through the inner ring. Where Square Maze has walls at the grid boundary, Circular Maze has ring-end wrap-around. The forced-move logic is identical; the shape of where that logic fires is different.
Hex Mazes use six directions on a hexagonal tiling — more routing freedom than four-direction variants. Hidato (Starlink) uses eight directions on a square grid with diagonal adjacency. Circular Maze sits alongside Square Maze in the four-direction family, distinguished by its radial topology rather than any change in constraint type.
THE SOLVE ORDER
- Orient: count cells per ring, note the inner ring size.
- Examine inner-ring clues and ring-1/ring-2 boundary clues first — the tightest constraints are here.
- Sort all gaps smallest-first. Force gap-0 (adjacent clues) and gap-1 segments immediately.
- After each placement, cascade dead-ends — scan for one-free-neighbour cells and resolve them.
- Verify that remaining empty cells are still connected; a pocket with one entry forces the path through it.
- Move to the next gap and repeat.
Most beginner Circular Mazes resolve completely from inner-ring forcing and dead-end cascades. The outer rings, with their larger cell counts and wrap-around freedom, fill in quickly once inner segments fix which numbers enter and leave each ring.